2.6. Certain computer coding systems use randomization to assign memory storage locations to account numbers. Suppose that N = MA different accounts are to be randomly located among M storage locations.

Let X; be the number of accounts assigned to the ith location. If the accounts are distributed independently and each location is equally likely to be chosen, show that Pr{X; = k} - e-"Ak/k! as N - oo. Show that X; and X; are independent random variables in the limit, for distinct locations i j. In the limit, what fraction of storage locations have two or more accounts assigned to them?